Added state methods to allow pickling of IFDRational

Tests/test_file_tiff.py

@@ -146,7 +146,8 @@ class TestFileTiff:
             "Tests/images/hopper_float_dpi_" + str(resolutionUnit) + ".tif"
         ) as im:
             assert im.tag_v2.get(RESOLUTION_UNIT) == resolutionUnit
-            assert im.info["dpi"] == (dpi, dpi)
+            for reloaded_dpi in im.info["dpi"]:
+                assert float(reloaded_dpi) == dpi
 
     def test_save_float_dpi(self, tmp_path):
         outfile = str(tmp_path / "temp.tif")
@@ -154,7 +155,8 @@ class TestFileTiff:
             im.save(outfile, dpi=(72.2, 72.2))
 
             with Image.open(outfile) as reloaded:
-                assert reloaded.info["dpi"] == (72.2, 72.2)
+                for dpi in reloaded.info["dpi"]:
+                    assert float(dpi) == 72.2
 
     def test_save_setting_missing_resolution(self):
         b = BytesIO()

src/PIL/TiffImagePlugin.py

@@ -358,6 +358,16 @@ class IFDRational(Rational):
             other = other._val
         return self._val == other
 
+    def __getstate__(self):
+        return [self._val, self._numerator, self._denominator]
+
+    def __setstate__(self, state):
+        IFDRational.__init__(self, 0)
+        _val, _numerator, _denominator = state
+        self._val = _val
+        self._numerator = _numerator
+        self._denominator = _denominator
+
     def _delegate(op):
         def delegate(self, *args):
             return getattr(self._val, op)(*args)